Total absolute curvature and tightness of noncompact manifolds

DOI10.1090/S0002-9947-96-01632-7zbMath0864.53043OpenAlexW1599168599MaRDI QIDQ4890012

Martin van Gemmeren

Publication date: 15 October 1996

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-96-01632-7

zbMATH Keywords

tightnessBetti numberstotal absolute curvatureproper Morse functionlimit directionChern-Lashof inequality

Mathematics Subject Classification ID

Higher-dimensional and -codimensional surfaces in Euclidean and related (n)-spaces (53A07) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Singularities of differentiable mappings in differential topology (57R45)

Related Items

The main theorem of discrete Morse theory for Morse matchings with finitely many rays, The number of critical elements of discrete Morse functions on non-compact surfaces, Total curvature of complete submanifolds of Euclidean space

Cites Work

• On the total curvature of immersed manifolds. II
• On total absolute curvature of nonclosed submanifolds
• Singular homology on an untriangulated manifold
• Taut immersions of non-compact surfaces into a Euclidean 3-space
• Minimal total absolute curvature for immersions
• Totale Absolutkrümmung in Differentialgeometrie und -topologie
• Morse Theorie für berandete Mannigfaltigkeiten. (Morse theory for bounded manifolds)
• Morse Theory. (AM-51)
• Ends of locally compact groups and their coset spaces
• Tightly Embedded 2-Dimensional Polyhedral Manifolds
• High Codimensional 0-Tight Maps of Spheres
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item